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valina [46]
3 years ago
5

Round 0.641 to the nearest hundredth. ​

Mathematics
1 answer:
mixas84 [53]3 years ago
4 0

Answer:

0.64

Step-by-step explanation:

Find the number in the hundredth place  4  and look one place to the right for the rounding digit  1 . Round up if this number is greater than or equal to  5  and round down if it is less than  5 .

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A cardboard box without a lid is to have a volume of 8,788 cm3. Find the dimensions that minimize the amount of cardboard used.
Montano1993 [528]

Answer:

  x = y = 26 cm; z = 13 cm

Step-by-step explanation:

The generic solution for the minimum material in an open-top box is that the box is square and half as high as it is wide. It is half a cube of twice the volume.

The dimensions of the square base are ...

  ∛(2·8788 cm³) = 26 cm

Then the height is half that, or 13 cm.

  x = y = 26 cm; z = 13 cm

_____

If you need to see the development, you can use the method of Lagrange multipliers to find the minimum area for the given volume;

  area = xy +2(xz +yz)

  volume = xyz = 8788

We require each of the partial derivatives of L with respect to x, y, z, and λ to be zero.

  L = xy +2(xz +yz) +λ(xyz -8788)

  partial with respect to x: 0 = y+2z +λyz

  partial with respect to y: 0 = x +2z +λxz

  partial with respect to z: 0 = 2x+2y +λxy

  partial with respect to λ: 0 = xyz -8788

From the first two equations, we have ...

  λ = (y +2z)/(yz) = 1/z +2/y

  λ = (x +2z)/(xz) = 1/z +2/x

Equating these expressions for λ, we find ...

  1/z +2/y = 1/z +2/x   ⇒   x = y

The third equation then tells us ...

  λ = (2x +2y)/(xy) = 2/y +2/x

Comparing this to either of the first two expressions for λ, we see ...

  1/z +2y = 2/x +2/y   ⇒   z = x/2

This is the result we started the answer with:

  x = y = 2z = ∛(2·8788 cm³)

7 0
2 years ago
The ratio of boys to girls in a class is 4 : 5
Fofino [41]

Answer: 4/9 of the class are boys and 5/9 of the class are girls.

Step-by-step explanation:

  1. There are 9 nine students in total in the class since 4 + 5 = 9.
  2. Input the amount of boys and girls there are in the class in the numerator  and have 9 as the denominator. 4/9 of the class are boys and 5/9 of the class are girls.
7 0
3 years ago
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7800 dollars is placed in an account with an annual interest rate of 6.5%. How much will be in the account after 29 years, to th
dimaraw [331]

Answer:

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Step-by-step explanation:

Base amount: $7,800.00

Interest Rate: 6.5% (yearly)

Effective Annual Rate: 6.5%

Calculation period: 29 years

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